Small divisors and large multipliers

We study germs of singular holomorphic vector fields at the origin of $\Bbb C^n$ of which the linear part is 1-resonant and which have a polynomial normal form. The formal normalizing diffeomorphism is usually divergent at the origin but there exists holomorphic diffeomorphisms in some "sectorial domains" which transform these vector fields into their normal form. In this article, we study the interplay between the small divisors phenomenon and the Gevrey character of the sectorial normalizing diffeomorphisms. We show that the Gevrey ordrer of the latter is linked to the diophantine type of the small divisors.Comment: 22 pages, to appear in Annales de l'Institut Fourie

Entrepreneurship and innovation

This report provides an overview of recent facts and figures on start-ups in the Netherlands, techno start-ups in particular and the overall link between entrepreneurship and innovation.

'The Babblings of Pragmatism':Reconstructing R.G. Collingwood's Rejection of F.C.S. Schiller's Pragmatism in Speculum Mentis

Despite R.G. Collingwood’s lifelong attempt to bring about a ‘rapprochement’ between theory and practice, his relation to pragmatism, the school that has the same central ambition, has hitherto been understudied. In particular, it remains unclear in the secondary literature why Collingwood felt necessitated to reject pragmatism himself. This paper partly remedies that gap by showing that, in Speculum Mentis, Collingwood interprets the pragmatist position as seeing relatively clearly into the nature of knowledge as consisting of questions and answers, but ultimately relying on a bifurcation of thought and will, a dualism it precisely set out to refute in the first place. Pragmatism, in other words, is incoherent. Moreover, Collingwood himself rejects the dualism between thought and will as well. Furthermore, I argue that Collingwood’s criticism is best understood as dealing with F.C.S. Schiller’s version of pragmatism. By relating Collingwood’s sparse remarks on the subject to the position of Schiller, enough meaning to the former can be given so as to render his refutation of pragmatism intelligible

All thought exists for the sake of action:the historical and philosophical relations between R.G. Collingwood and classical pragmatism

Was R.G. Collingwood (1889-1943) an ‘undercover pragmatist’, as some have suggested? Or did he rather consider pragmatism to be one of his ‘least favorite varieties of philosophy’, as others have held? This book carves out a middle path between these opposing views. It shows that Collingwood argues that, for a variety of reasons, pragmatism fails to achieve its ostensible ideal of overcoming the dualism of theory and practice. In its stead Collingwood elaborates his own philosophy, in which thought and action are really united. Hence, instead of accepting or rejecting pragmatism wholesale, he would have regarded himself as more of a pragmatist than the pragmatists themselves

Integral multidisciplinary rehabilitation treatment planning

This paper presents a methodology to plan treatments for rehabilitation outpatients. These patients require a series of treatments by therapists from various disciplines. In current practice, when treatments are planned, a lack of coordination between the different disciplines, along with a failure to plan the entire treatment plan at once, often occurs. This situation jeopardizes both the quality of care and the logistical performance. The multidisciplinary nature of the rehabilitation process complicates planning and control. An integral treatment planning methodology, based on an integer linear programming (ILP) formulation, ensures continuity of the rehabilitation process while simultaneously controlling seven performance indicators including access times, combination appointments, and therapist utilization. We apply our approach to the rehabilitation outpatient clinic of the Academic Medical Center (AMC) in Amsterdam, the Netherlands. Based on the results of this case, we are convinced that our approach can be valuable for decision-making support in resource capacity planning and control at many rehabilitation outpatient clinics. The developed model will be part of the new hospital information system of the AMC

Flexible nurse staffing based on hourly bed census predictions

Workload on nursing wards depends highly on patient arrivals and patient lengths of stay, which are both inherently variable. Predicting this workload and staffing nurses accordingly is essential for guaranteeing quality of care in a cost effective manner. This paper introduces a stochastic method that uses hourly census predictions to derive efficient nurse staffing policies. The generic analytic approach minimizes staffing levels while satisfying so-called nurse-to-patient ratios. In particular, we explore the potential of flexible staffing policies which allow hospitals to dynamically respond to their fluctuating patient population by employing float nurses. The method is applied to a case study of the surgical inpatient clinic of the Academic Medical Center (AMC) Amsterdam. This case study demonstrates the method's potential to study the complex interaction between staffing requirements and several interrelated planning issues such as case mix, care unit partitioning and size, and surgical block planning. Inspired by the numerical results, the AMC decided that this flexible nurse staffing methodology will be incorporated in the redesign of the inpatient care operations during the upcoming years